What is the sum of the two integers between which $\frac{\sqrt{17}}{2}$ lies?
Since 17 is between 16 and 25, $\sqrt{17}$ is between $\sqrt{16}=4$ and $\sqrt{25}=5$. Then, $\frac{\sqrt{17}}{2}$ is between $\frac{4}{2}=2$ and $\frac{5}{2}=2.5$. This means that the two integers between which $\frac{\sqrt{17}}{2}$ lies are 2 and 3. The sum of these integers is $2+3=\boxed{5}$.